Kamal Hajian

Middle East Technical University | METU · Department of Physics

The geometries with SL$(2,\mathbb{R})$ and some axial U$(1)$ isometries are called ``near-horizon extremal geometries" and are found usually, but not necessarily, in the near-horizon limit of the extremal black holes. We present a new member of this family of solutions in five-dimensional Einstein-Hilbert gravity that has only one non-zero angular...

In gauge invariant theories, like Einstein-Maxwell theory, physical observables should be gauge invariant. In particular, mass, entropy, angular momentum, electric charge, and their respective chemical potentials, temperature, horizon angular velocity, and electric potential, which appear in the laws of black hole thermodynamics, should be gauge in...

In gauge invariant theories, like Einstein-Maxwell theory, physical observables should be gauge invariant. In particular, mass, entropy, angular momentum, electric charge and their respective chemical potentials, temperature, horizon angular velocity and electric potential which appear in the laws of black hole thermodynamics should be gauge invari...

Black hole firewall paradox is an inconsistency between four postulates in black hole physics: (1) the unitary evolution in quantum systems, (2) application of the semi-classical field theory in low curvature backgrounds, (3) statistical mechanical origin of the black hole entropy, and (4) the equivalence principle in the version of no drama for fr...

Einstein observers in flat space-time are inertial observers which use light to synchronize their clocks. For such observers, speed of light is a constant by construction. However, one can use super-translations to change coordinates from Einstein to BMS coordinates. From the point of view of BMS observers, speed of light is not a constant all over...

The first law of black hole thermodynamics in the presence of a cosmological constant Λ can be generalized by introducing a term containing the variation δΛ. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge, etc., it has been shown [Classical Quant. Grav. 3...

The first law of black hole thermodynamics in the presence of a cosmological constant $\Lambda$ can be generalized by introducing a term containing the variation $\delta \Lambda$. Similar to other terms in the first law, which are variations of some conserved charges like mass, entropy, angular momentum, electric charge etc., it has been shown in [...

It has been observed that for black holes in certain family of Horndeski gravity theories Wald's entropy formula does not lead to the correct first law for black hole thermodynamics. For this family of Horndeski theories speeds of propagation of gravitons and photons are in general different and gravitons move on an effective metric different than...

It has been observed that for black holes in certain family of Horndeski gravity theories Wald's entropy formula does not lead to the correct first law for black hole thermodynamics. For this family of Horndeski theories speeds of propagation of gravitons and photons are in general different and gravitons move on an effective metric different than...

Einstein observers in flat space-time are inertial observers which use light to synchronize their clocks. For such observers, speed of light is a constant by construction. However, one can impose BMS super-translations on flat space-time and the Einstein observers to introduce BMS observers. From the point of view of BMS observers, speed of light i...

We present a one-function family of solutions to 4D vacuum Einstein equations. While all diffeomorphic to the same extremal Kerr black hole, they are labeled by well-defined conserved charges and are hence distinct geometries. We show that this family of solutions forms a phase space the symplectic structure of which is invariant under a U(1) Kac-M...

Cosmological constant can be considered as the on-shell value of a top form in gravitational theories. In this context, we show that it is conserved charge of global part of the gauge symmetry, irrespective of the dynamics of the metric and other fields. In addition, we introduce its conjugate chemical potential, and prove the corresponding general...

We present a one-function family of solutions to 4D vacuum Einstein equations. While all diffeomorphic to the same extremal Kerr black hole, they are labeled by well-defined conserved charges and are hence distinct geometries. This family of solutions form the "Extremal Kerr Phase Space". We show the symplectic structure of this phase space remains...

A simple xAct example: the Kerr-Newman black hole and its conserved charges which are calculated by the ”solution phase space method”. The file can be used as a pedagogical code for using xAct.

Black holes as solutions to gravity theories, are generically identified by a set of parameters. Some of these parameters are associated with black hole physical conserved charges, like ADM charges. There can also be some "redundant parameters." We propose necessary conditions for a parameter to be physical. The conditions are essentially integrabi...

Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called ``solution phase space method," conserved charges are unambiguous and regular. Moreover, assumin...

Recently, a general formulation for calculating conserved charges for (black hole) solutions to generally covariant gravitational theories, in any dimensions and with arbitrary asymptotic behaviors has been introduced. Equipped with this method, which can be dubbed as "solution phase space method," we calculate mass and angular momentum for the Ker...

We provide a simple way for calculating the entropy of a Schwarzschild black hole from the entropy of its Hawking radiation. To this end, we show that if a thermodynamic system loses its energy only through the black body radiation, its loss of entropy is always 3/4 of the entropy of the emitted radiation. This proposition enables us to relate the...

We provide a general formulation for calculating conserved charges for solutions to generally covariant gravitational theories with possibly other internal gauge symmetries, in any dimensions and with generic asymptotic behaviors. These solutions are generically specified by a number of exact (continuous, global) symmetries and some parameters. We...

Considering the role of black hole singularity in quantum evolution, a resolution to the firewall paradox is presented. It is emphasized that if an observer has the singularity as a part of his spacetime, then the semi-classical evolution would be non-unitary as viewed by him. Specifically, a free-falling observer inside the black hole would have a...

Near Horizon Extremal Geometries (NHEG), are geometries which may appear in the near horizon region of the extremal black holes. These geometries have $SL(2,\mathbb{R})\!\times\!U(1)^n$ isometry, and constitute a family of solutions to the theory under consideration. In the first part of this report, their thermodynamic properties are reviewed, and...

We construct the classical phase space of geometries in the near-horizon region of vacuum extremal black holes as announced in [arXiv:1503.07861]. Motivated by the uniqueness theorems for such solutions and for perturbations around them, we build a family of metrics depending upon a single periodic function defined on the torus spanned by the $U(1)...

We construct the NHEG phase space, the classical phase space of Near-Horizon Extremal Geometries with fixed angular momenta and entropy, and with the largest symmetry algebra. We focus on vacuum solutions to $d$ dimensional Einstein gravity. Each element in the phase space is a geometry with $SL(2,R)\times U(1)^{d-3}$ Killing isometries which has v...

In arXiv:1310.3727 we formulated and derived the three universal laws governing Near Horizon Extremal Geometries (NHEG). In this work we focus on the Entropy Perturbation Law (EPL) which, similarly to the first law of black hole thermodynamics, relates perturbations of the charges labeling perturbations around a given NHEG to the corresponding entr...

Near Horizon Extremal Geometries (NHEG) are solutions to gravity theories with SL(2;R) cross U(1) to some power n symmetry, are smooth geometries and have no event horizon, unlike black holes. Following the ideas by R. Wald, we derive laws of NHEG dynamics, the analogs of laws of black hole dynamics for the NHEG. Despite the absence of horizon in t...