Is there a change in mass of a black hole when it swallows an object ?

Black holes have different masses depending on the amount of mass they "swallowed". E.g., the massive black holes in the centres of galaxies comprise millions to billions of solar masses. However, the process of accretion of mass by a black hole creates radiation, and therefore part of the original "swallowed" mass will be lost. See., e.g. https://en.wikipedia.org/wiki/Accretion_disk.

The short answer is yes and no, depending upon the position of the particle. The mass adds up as a unit of entropy to the black hole but it does not cause the black hole to gain mass. This causes an increase in the entropy of the black hole which can be calculated with the help of the equation- dS= 8(pi)*M*dm. Also the Schwarzschild radius of the black hole keeps getting bigger by the accretion of mass around the event horizon, that's why until the particle is annihilated at the event horizon it contributes an increase in Schwarzschild radius of the black hole but after crossing the event horizon it just become a part of the entropy of the black hole. You can also refer to these links: https://en.wikipedia.org/wiki/Black_hole_thermodynamics

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Regards

Rishi

Yes the mass increases. Mass of the original BH + Stars swallowed by the BH = mass of the final BH.

You can easily see this in the concept of absolute and apparant horizon in Finkelstein coordinates.

Wolfgang R. Dick "the process of accretion of mass by a black hole creates radiation, and therefore part of the original "swallowed" mass will be lost."

Your use of "swallowed" is unconventional here. People normally use the term "swallowed" to mean "passed inside the event horizon". So matter in the accretion disk, emitting radiation and plasma jets, has not been swallowed yet.

Ray Butler : Indeed, this is what I meant, but my wording was not very precise. Compared to the original mass, the "swallowed" mass is lower because radiation was created during the accretion process. And I understand that this is a very rough, rather popular description.

If the mass of the object that enters is low enough that all of it can enter at once, so there is no "accretion" to worry about, the result is as stated by Bhattacharjee is correct: the original mass of the black hole plus the original mass of the object entering the event horizon is equal to the final mass of the black hole. This would certainly be true of things like asteroids, and for supermassive black holes, perhaps even small stars, if they approached it at a high velocity.

However, it is true, as implied in other answers, that if the infalling mass is, like trying to push an elephant through a keyhole, too big to all fall in at once, or if the relative velocity is low enough that the infalling mass is tidally disrupted, then you will get an accretion disk surrounding the black hole, in which the infalling mass in the outer part of the disk compresses the infalling mass in the inner part of the disk, heating it to extremely high temperatures, and causing an emission of radiation that may turn as much as 70% of the infalling mass into radiation, per Einstein's equation E = m c-squared. So for large objects slowly approaching even a supermassive black hole, part of the infalling mass may be lost before it can reach the event horizon. However, the mass of whatever part of the infalling object actually manages to pass through the event horizon will be added to the original mass of the black hole.

To summarize, whatever mass is actually "swallowed" by the black hole is simply added to the oriiginal mass of the black hole. That may not be as much as the original mass of the additional object, but the mass of what IS swallowed is equal to the increase in mass of the black hole.

Observations of binary mergers of a black hole (BH) with another BH or a neutron star (NS) produce gravitational waves (GWs) detected by the LIGO mission. While general relativity is required to follow the inspiral of the two spinning masses to merger, a quasi-Newtonian analysis of the first detected event, GW150914, is given by the 950 team members here: https://arxiv.org/abs/1608.01940.

As summarized by Wikipedia (https://en.wikipedia.org/wiki/First_observation_of_gravitational_waves), this event is modeled as a BH binary with initial masses of 35 and 30 solar masses, and a resulting mass of 62 solar masses. The 'missing' mass was converted to energy in GWs equaling 3 solar masses x c^2.

More recent GW detections by LIGO, Virgo and KAGRA missions of BH-NS mergers were modeled as BH masses between 6-9 solar masses and NS masses between 1.5-1.9 solar masses, with resulting BH masses between 7-11 solar masses. Again, the 'missing' masses were converted to energy in GWs equaling between 0.5-2 solar masses x c^2. This data is summarized in a technical paper: https://iopscience.iop.org/article/10.3847/2041-8213/ac082e

Recall that the radiant energy produced by most stars from proton-proton reactions is about 0.007 solar masses x c^2, so the GW energy releases via GWs is far larger.

All contributions above ignore the negative energy contained in the gravitational field around a black hole. The gravitational energy is proportional to the mass squared and is, as already mentioned, negative.

A new mass M falling into the black hole therefor can generate radiation which exceeds Mc².

Another possibility is, that a limit for the strength of a gravitational field exists.

If this is the case, we must reconsider all cosmology theories.

A possible approach to that limit is the assumption that a negative absolute value for the energy density is not allowed. This implies a strong cosmic gravitational field of positive energy density which overcompensates the energy density of gravitational fields up to the strength at the surface of neutron stars.

This approach has dramatic consequences for cosmology theories.

A black hole is an object whose radius is equal to the Schwarzschild radius r_g = 2GM / c ^ 2. From the point of view of a physical observer, time stops on the surface of a black hole. A physical observer, who perceives time as a continuous stream of events in 3-space, cannot catch the processes taking place inside the black hole, since the region r <r_g does not belong to the real 3-space. However, some events occurring in real 3-space, where r> r_g, under certain conditions can become observable. In principle, phenomena associated with the convergence of a black hole with physical bodies of 3-space, for example, with stars, can be observed. In the framework of modern concepts, the rapprochement (collision) of a black hole with material objects can cause a number of disturbances in physical 3-space up to partial or complete absorption of physical objects.

A deeper study of the problem of bodies belonging to the worlds, in principle differing from the 3-dimensional space through which time flows, requires closer attention to the problem of Time. In general relativity, Time is simply the fourth coordinate, the tangent vector to which has an imaginary length. We can mentally imagine worlds where bodies have negative and imaginary masses. But the rapid changes in conditions on the planet urgently require people to change their state of consciousness in order to be able to respond to these changes. For this, it is necessary to stop perceiving Time only as a measure of measuring the speed of various physical processes. To do this, it is necessary to stop constantly referring to the fact that Einstein allegedly did not complete something in his theory of relativity, limiting the field of its application to only 4-dimensional Riemannian space. But all this was 100 years ago! Science could well reach a higher level of perception of the structure of space-time, if not for the massive desire to reason within the framework of the old theory about what it does not allow. This reluctance to view the world for a new perspective leads to a collective denial of all experiments that go beyond what can be explained in terms of general relativity. True, scientists were initially carried away by Mandelbrot's theory of fractals. But this really beautiful representation system only applies to 3-space. And all these unthinkable patterns and weaves are created by Time itself. Experimental substantiations of the fractal structure of Time were obtained by Professor Shnoll, But they were not noticed by physicists, and biologists insistently demanded that he smooth the peaks of his graphs (obtained experimentally!), So that the results would correspond to generally accepted views, in particular, the Gaussian distribution. Shnoll proved that time is fractal in each of its periods of any length. Cosmic bodies have their own periods, which we perceive as periods of rotation of bodies around their axes and central bodies. Time does not flow evenly from the future to the past; at every moment it creates the material world, which we call the present. The uniformity of the flow of time is the result of observing the movements of the Sun and stars. However, the very perception of Time also depends on the state and its location and the person himself. So the life of every creature in the Universe is a continuous chain of the totality of events of different bodies and lungs of Nature: Everything consists of in and Everything depends on Everything.

The question mixes a theoretical object, the black hole, swallowing an unexplained, undefined property, meaning mass. How does one predict how something unexplained can be swallowed by another something, a black hole, that's existence is unsubstantiated by direct empirical evidence.

No one has ever measured either time or space. Both pretended measurements are object-related measurements. No one has ever written a physics equation that contained the direct representation of either space or time. Both have always been substituted for by object-related measurement rules.

Mass was chosen to be the third indefinable property of physics. It is heavily involved in relationships with later introduced properties. None of those relationships tells us what only direct empirical evidence can tell us "What is mass"?

The answer I give to the main proposed question is to rely upon the accuracy of patterns found in effects that are modeled mathematically by physics equations. The patterns of change are accurately modeled. The variables, some of which are invented, do not prevent successful predictions. The imaginative mathematics of theoretical physics, i.e., shortcuts for counting that which is imagined to exist, will add up successfully in magnitudes. One can always imagine the existence of the solution.

Definitions no longer are strict. Rules of measurement and explanations for what properties do, or are imagined to do, are accepted as explanations for what a property is. Variables are added as needed to keep the mathematics developing. Theoretical physicists supply reasons to invent them in their quest to move closer to theoretically achieving fundamental unity.

Unfortunately, fundamental unity was excluded from physics at the introduction of f=ma when mass was made the third indefinable property of physics. Disunity was fortified by the decision to make temperature the fourth indefinable property, and, by only counting electric charge.

James A Putnam

My answer and the mainstream answer are the same. Except for its appearance, a black hole is the same as any other star. It has a mass-equivalence to it. When something falls into it its mass accordingly increases. This answer is only theoretical since no such before and after analysis have been done.

Larissa Borissova "...the region r <r_g does not belong to the real 3-space"

The gravitational impact of the mass inside this region belongs to the real 3-space.

It is true, that we cannot investigate this region. But we cannot say that it is out of time and space. The Schwarzschild surface of a black hole is not the passage into a new kind of space like the passage into a wonderland.

We assign a low matter density to big black holes, and we consider black holes as collapsed neutron stars with an extremely high density.

This means there is something inside this region, which we do not understand.

The missing understanding has something to do with the negative energy density of gravitational fields. Allegedly the gravitational energy density is not contained in Einstein’s field equations. In the low energy case, this may be true or not. But it is sure that something is missing in those equations which would allow to describe the nonlinear high energy case.

Gravitational Waves are believed to be produced by the merger of two Black Holes or a Black Hole and a Neutron star. But Black Holes do not physically exist anywhere in the universe, they are just a mathematical fantasy, a novel creation of human ignorance.

An invalid assumption regarding the non-interacting characteristic of electrons, protons and ions constitutes the very foundation upon which the marvels of Black Holes and Neutron Stars are created through current models of gravitational collapse of massive stellar cores.

In a degenerate stellar body, where active nuclear fusion reactions have already stopped and thermal pressure reduced due to cooling, the electron degeneracy pressure is said to support the stellar body against its gravitational collapse. Firstly, even if we assume that the degenerate electrons (somehow) acquire high kinetic energies through the action of QM principles, such Fermi gas or electron gas does not satisfy the basic assumptions of the kinetic theory. Secondly, even if we assume that such high energy electron gas does acquire the well known electron degeneracy pressure through high momentum exchange among electron particles, such degeneracy pressure cannot support the gravitational in-fall of massive positive ions just because electrons cannot exchange momentum with positive ions through elastic collisions to push them outwards.

As in kinetic theory of gases, high energy 'free' electron 'particles' are supposed to generate kinetic pressure by exchanging their momentum in elastic collisions. This is the fundamental basis of the notion of 'electron degeneracy pressure' in Astrophysics. When a solid iron core becomes degenerate, the degenerate electrons get freed from their parent iron atoms leaving behind 'positive ions' of iron. When the positive ions start falling towards the center of the core under gravity, the high energy degenerate electrons are supposed to push these ions outwards by their degeneracy pressure to counter the effect of gravity. However, to impart an outward push to the falling ions, the high energy degenerate electrons will have to exchange their momentum with the falling ions through elastic collisions. But the high energy electrons can exchange their momentum with positive ions through elastic collisions ONLY IF all electrons and ions are assumed to be non-interacting. Actually however, because of their electrostatic interactions, the electrons can never exchange their momentum with positive ions and hence can never provide the so-called electron degeneracy pressure in stellar cores to counter the effect of gravity.

The main reason for ASSUMING the electron degeneracy pressure in solid iron stellar cores is the implied belief that a cooled down stellar core cannot maintain its Hydrostaic equilibrium in the absence of adequate thermal pressure and that nothing else can stop the gravitational collapse of such cores. But why do we need to apply Hydrostatic equilibrium conditions for stability of a SOLID iron core? That is because in Astrophysics, all constituents of stellar cores are always assumed to be non-interacting free particles obeying the equations of Kinetic Theory of gases. In current models, the stresses in a solid iron stellar core are never analyzed as a SOLID body under self-gravitation, by using the Equilibrium equations of elasticity.

Therefore, the constituents of a solid stellar core are first ASSUMED to be non-interacting for applying Hydrostatic equilibrium equations and then the electrons and ions are again ASSUMED to be non-interacting for invoking the electron degeneracy pressure to support the pull of gravity.

Hence, it turns out that all stellar cores which are said to be degenerate, where some sort of degeneracy pressure is invoked to prevent their gravitational collapse under Hydrostatic equilibrium conditions, are in fact SOLID stellar cores which acquire their stability through Equilibrium equations of elasticity. For the stability of a solid iron core under self-gravitation, neither do we need to assume non-interacting characteristic of the core constituents for applying Hydrostatic equilibrium equations, nor do we need to invoke the fictitious electron degeneracy pressure. All we need is to apply Equilibrium equations of elasticity for working out the radial and hoop stresses in the spherically symmetric solid iron body under self-gravitation. It is found that the radial and hoop stresses in the solid iron stellar body are always minimum at the center and maximum at the periphery of the body. This shows that solid stellar cores can never collapse under self-gravitation.

Unfortunately, our Astrophysicists are not exposed to Theory of Elasticity in general and working out stresses and strains in SOLID bodies in particular and this ignorance is the root cause of creation of fictitious Black Holes.

Dear Gurcharn Singh Sandhu

Your explanations about processes in the interior of stars uses terms of ideal gas theory. But actually, nuclear physics terms are needed.

Schwarzschield BlacK holl is the object whose gravitational radius r_g = 2GM/c^2. Its mass can be more if it swallows material objects. Because its gravitational radius r_g = 2GM/c^2, its radius r_g will be more alsoIt is evidently that the mass of black hole must be greate tha to absorb the part of mass of another stars/

There exist two kinds of black holes: 1) Schwarzscield kind where r_g = 2GM/c^2 << a (a is its radius), 20 quickly rotating neutron stars in the state of collapse, for which r_g = a. The increasing of mass in the first case is more probably for very massiv stars with greate radius a. The second case can be realized also for qutckly rotating stars.

If A "Black Hole" swallows an object, How the claims of these two professors are justifiable?

Of course there are changes in black holes when they absorb objects: they become thicker before they explode to big-bangs.