[Show abstract][Hide abstract] ABSTRACT: A spacetime is locally flat if and only if no geodesical deviation exists for congruences of all kinds of geodesics. However, while for causal geodesics the deviation can be measured observing the motion of (infinitesimal) falling bodies, it does not seem possible to evaluate the geodesical deviation of spacelike geodesic. So a physical problem may arise. To tackle this problem we analyze the interplay of local flatness and geodesic deviation measured for causal geodesics. We establish that a generic spacetime is (locally) flat if and only if there is no geodesic deviation for timelike geodesics or, equivalently, there is no geodesic deviation for null geodesics.
Frontiers in Physics 09/2013; 1. DOI:10.3389/fphy.2013.00012
[Show abstract][Hide abstract] ABSTRACT: Much attention has been recently devoted to modified theories of gravity in
the attempt to efficiently describe both early inflation and late-time
acceleration of our universe without referring to the cosmological constant or
other ad hoc kinds of fluids. The simplest models overcome General Relativity
simply by replacing $R$ with $F(R)$ in the Einstein--Hilbert action.
Unfortunately, such models typically lack most of the beautiful solutions
discovered in Einstein's gravity. Nonetheless, in $F(R)$ gravity, it has been
possible to get at least few black holes, but still we do not know any empty
wormhole-like spacetime solution. The present paper aims to explain why it is
so hard to get such solutions (given that they exist). Few solutions are
derived in the simplest cases while only an implicit form has been obtained in
the non-trivial case.
[Show abstract][Hide abstract] ABSTRACT: In the present paper, Unruh--DeWitt detectors are used in order to
investigate the issue of temperature associated with a spherically symmetric
dynamical space-times. Firstly, we review the semi-classical tunneling method,
then we introduce the Unruh--DeWitt detector approach. We show that for the
generic static black hole case and the FRW de Sitter case, making use of
peculiar Kodama trajectories, semiclassical and quantum field theoretic
techniques give the same standard and well known thermal interpretation, with
an associated temperature, corrected by appropriate Tolman factors. For a FRW
space-time interpolating de Sitter space with the Einstein--de Sitter universe
(that is a more realistic situation in the frame of $\Lambda$CDM cosmologies),
we show that the detector response splits into a de Sitter contribution plus a
fluctuating term containing no trace of Boltzmann-like factors, but rather
describing the way thermal equilibrium is reached in the late time limit. As a
consequence, and unlike the case of black holes, the identification of the
dynamical surface gravity of a cosmological trapping horizon as an effective
temperature parameter seems lost, at least for our co-moving simplified
detectors. The possibility remains that a detector performing a proper motion
along a Kodama trajectory may register something more, in which case the
horizon surface gravity would be associated more likely to vacuum correlations
than to particle creation.
International Journal of Theoretical Physics 11/2011; 51(5). DOI:10.1007/s10773-011-1033-2 · 1.18 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The aim of this work is to review the tunnelling method as an alternative
description of the quantum radiation from black holes and cosmological
horizons. The method is first formulated and discussed for the case of
stationary black holes, then a foundation is provided in terms of analytic
continuation throughout complex space-time. The two principal implementations
of the tunnelling approach, which are the null geodesic method and the
Hamilton-Jacobi method, are shown to be equivalent in the stationary case. The
Hamilton-Jacobi method is then extended to cover spherically symmetric
dynamical black holes, cosmological horizons and naked singularities. Prospects
and achievements are discussed in the conclusions.
[Show abstract][Hide abstract] ABSTRACT: In the paper, the temperature associated with a dynamical spherically
symmetric black hole or with a cosmological horizon is investigated from the
point of view of a point-like detector. First, we briefly review the
Hamilton-Jacobi tunneling method for a generic dynamical spherically symmetric
space-time, and present two applications of the tunneling method. Then, we
apply a well-known relativistic quantum theoretical technique, namely the
Unruh-DeWitt detector formalism for a conformally coupled scalar field in a
generic FRW space-time. As an application, for the generic static black hole
case and the FRW de Sitter case, making use of peculiar Kodama observer
trajectories, the tunneling semiclassical results are fully recovered,
automatically corrected by Tolman factors. Some remarks on the temperature of
FRW universe are presented. For more general spaces interpolating de Sitter
space with the Einstein-de Sitter universe a second set of poles is present,
whose exact role remains to be clarified, plus an extra fluctuating term
describing the way equilibrium is reached, similarly to de Sitter space. The
simple thermal interpretation found for de Sitter space is lost and forces, at
a same time, a different quantum interpretation of the horizon surface gravity
for the cosmological FRW models.
[Show abstract][Hide abstract] ABSTRACT: We give an interpretation of the temperature in de Sitter universe in terms
of a dynamical Unruh effect associated with the Hubble sphere. As with the
quantum noise perceived by a uniformly accelerated observer in static
space-times, observers endowed with a proper motion can in principle detect the
effect. In particular, we study a "Kodama observer" as a two-field Unruh
detector for which we show the effect is approximately thermal. We also
estimate the back-reaction of the emitted radiation and find trajectories
associated with the Kodama vector fields are stable.
Modern Physics Letters A 11/2010; DOI:10.1142/S0217732311036516 · 1.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Studying the behaviour of a quantum field in a classical, curved, spacetime is an extraordinary task which nobody is able to take on at present time. Independently by the fact that such problem is not likely to be solved soon, still we possess the instruments to perform exact predictions in special, highly symmetric, conditions. Aim of the present contribution is to show how it is possible to extract quantitative information about a variety of physical phenomena in very general situations by virtue of the so-called Hamilton-Jacobi method. In particular, we shall prove the agreement of such semi-classical method with exact results of quantum field theoretic calculations. Comment: To appear in the proceedings of "Cosmology, the Quantum Vacuum, and Zeta Functions": A workshop with a celebration of Emilio Elizalde's Sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 2010
[Show abstract][Hide abstract] ABSTRACT: The dark energy issue is focusing the attention of an incresing number of
physicists all over the world. Among the possible alternatives in order to
explain what as been named the "Mystery of the Millennium" are the so-called
Modified Theories of Gravity. A crucial test for such models is represented by
the existence and (if this is the case) the properties of their black hole
solutions. Nowadays, to our knowledge, only two non-trivial, spherically
symmetric, solutions with vanishing cosmological constant are known by Barrow &
Clifton (2005) and Deser, Sarioglu & Tekin (2008). Aim of the paper is to
discuss some features of such solutions, with emphasis on their thermodynamic
properties such as entropy and temperature, little progress being possible
along the way which leads to a consistent definition of mass.
[Show abstract][Hide abstract] ABSTRACT: Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunnelling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions of the sign of energy. PACS numbers:
[Show abstract][Hide abstract] ABSTRACT: Following recent literature on dS instability in presence of interactions, we study the decay of massive particles in general FRW models and the emission from naked singularities either associated with 4D charged black holes or with 2D shock waves, by means of the Hamilton--Jacobi tunneling method. It is shown that the two-dimensional semi-classical tunneling amplitude from a naked singularity computed in that way is the same as the one-loop result of quantum field theory. Comment: LaTex document, 14 pages, two figures
Journal of High Energy Physics 01/2010; 2010(5). DOI:10.1007/JHEP05(2010)092 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The arguments of the above article [arXiv:0910.3934] do not apply to the
papers which it criticizes, and contain several key errors, including a
fundamental misunderstanding about the equivalence principle.
[Show abstract][Hide abstract] ABSTRACT: We point out basic misunderstandings about quantum field theory, general
relativity and partial derivatives in the above Comments. In reply to a
second comment on our first reply by the same author, we also identify
precisely where the author's original calculation goes wrong and correct
it, yielding the same local Hawking temperature as obtained by the
Hamilton-Jacobi method.
[Show abstract][Hide abstract] ABSTRACT: Motivated by the considerable success of alternative theories of gravity, we consider the toy model of a higher derivative Lagrangian theory, namely the Pais-Uhlenbeck oscillator studied in a recent paper by Hawking-Hertog. Its Euclidean Path Integral is studied with a certain detail and a pedagogical derivation of the propagator, which makes use of a Theorem due to Forman, is consequently proposed Comment: 12 pages, no figures, error sign corrected in section 3, conclusions unchanged, one reference added
[Show abstract][Hide abstract] ABSTRACT: Previous work on dynamical black hole instability is further elucidated within the Hamilton-Jacobi method for horizon tunneling and the reconstruction of the classical action by means of the null-expansion method. Everything is based on two natural requirements, namely that the tunneling rate is an observable and therefore it must be based on invariantly defined quantities, and that coordinate systems which do not cover the horizon should not be admitted. These simple observations can help to clarify some ambiguities, like the doubling of the temperature occurring in the static case when using singular coordinates, and the role, if any, of the temporal contribution of the action to the emission rate. The formalism is also applied to FRW cosmological models, where it is observed that it predicts the positivity of the temperature naturally, without further assumptions on the sign of the energy. Comment: Standard Latex document, typos corrected, refined discussion of tunneling picture, subsection 5.1 removed
[Show abstract][Hide abstract] ABSTRACT: A local Hawking temperature is derived for any future outer trapping horizon in spherical symmetry, using a Hamilton Jacobi variant of the Parikh Wilczek tunneling method. It is given by a dynamical surface gravity as defined geometrically. The operational meaning of the temperature is that Kodama observers just outside the horizon measure an invariantly redshifted temperature, diverging at the horizon itself. In static, asymptotically flat cases, the Hawking temperature as usually defined by the Killing vector agrees in standard cases, but generally differs by a relative redshift factor between the horizon and infinity, this being the temperature measured by static observers at infinity. Likewise, the geometrical surface gravity reduces to the Newtonian surface gravity in the Newtonian limit, while the Killing definition instead reflects measurements at infinity. This may resolve a long-standing puzzle concerning the Hawking temperature for the extremal limit of the charged stringy black hole, namely that it is the local temperature which vanishes. In general, this confirms the quasi-stationary picture of black-hole evaporation in early stages. However, the geometrical surface gravity is generally not the surface gravity of a static black hole with the same parameters.
[Show abstract][Hide abstract] ABSTRACT: A local Hawking temperature was recently derived for any future outer trapping horizon in spherical symmetry, using a Hamilton-Jacobi tunneling method, and is given by a dynamical surface gravity as defined geometrically. Descriptions are given of the operational meaning of the temperature, in terms of what observers measure, and its relation to the usual Hawking temperature for static black holes. Implications for the final fate of an evaporating black hole are discussed. Comment: 7 pages, contribution to Proceedings of ERE2008
[Show abstract][Hide abstract] ABSTRACT: The instability against emission of fermionic particles by the trapping horizon of an evolving black hole is analyzed and confirmed using the Hamilton-Jacobi tunneling method. This method automatically selects one special expression for the surface gravity of a changing horizon. The results also apply to point masses embedded in an expanding universe. As a bonus of the tunneling method, we gain the insight that the surface gravity still defines a temperature parameter as long as the evolution is sufficiently slow that the black-hole pass through a sequence of quasi-equilibrium states, and that black holes should be semi-classically unstable even in a hypothetical world without bosonic fields.
[Show abstract][Hide abstract] ABSTRACT: We analyze the interplay of local flatness and geodesic deviation measured for causal geodesics starting from the remark that, form a physical viewpoint, the geodesic deviation can be measured for causal geodesic, observing the motion of (infinitesimal) falling bodies, but it can hardly be evaluated on spacelike geodesics. We establish that a generic spacetime is (locally) flat if and only if there is no geodesic deviation for timelike geodesics or, equivalently, there is no geodesic deviation for null geodesics.