black holes: Universal versus Killing horizons

Physical Review D, 2014

Black Holes in Lorentz violating theories A. Einstein-AEther theory B. Hořava-Lifshitz gravity C. Einstein-AEther black holes D. A digression on acoustic gravity and Universal horizons III. Physical trajectories in an Einstein-AEther black hole A. Ray tracing and peeling in purely metric black holes B. Rays of constant aether time C. Modified dispersion relations D. A notion of conserved energy E. Physical ray trajectories IV. Near-horizon physics A. Near the Universal horizon B. Near the Killing horizon C. Lingering near the Killing horizon V. Hawking Radiation? VI. Discussion

Journal of High Energy Physics, 2021

The persistence of a suitable notion of black hole thermodynamics in Lorentz breaking theories of gravity is not only a non-trivial consistency test for such theories, it is also an interesting investigation per se, as it might help us identifying the crucial features at the root of these surprising laws governing such purely gravitational objects. In past investigations, controversial findings were presented in this sense. With the aim of settling this issue, we present here two complementary derivations of Hawking radiation in geometries endowed with universal horizons: a novel feature of back holes in Lorentz breaking theories of gravity which reproduces several properties normally characterizing Killing horizons. We find that both the derivations agree on the fact that the Hawking temperature associated to these geometries is set by the generalized universal horizon peeling surface gravity, as required for consistency with extant derivations of the first law of thermodynamics fo...

Physical Review D, 2012

Modified gravity models such as Hořava-Lifshitz gravity or Einstein-aether theory violate local Lorentz invariance and therefore destroy the notion of a universal light cone. Despite this, in the infrared limit both models above possess static, spherically symmetric solutions with "universal horizons" -hypersurfaces that are causal boundaries between an interior region and asymptotic spatial infinity. In other words, there still exist black hole solutions. We construct a Smarr formula (the relationship between the total energy of the spacetime and the area of the horizon) for such a horizon in Einstein-aether theory. We further show that a slightly modified first law of black hole mechanics still holds with the relevant area now a cross-section of the universal horizon. We construct new analytic solutions for certain Einstein-aether Lagrangians and illustrate how our results work in these exact cases. Our results suggest that holography may be extended to these theories despite the very different causal structure as long as the universal horizon remains the unique causal boundary when matter fields are added.

Classical and Quantum Gravity, 1998

It is a deceptively simple question to ask how acoustic disturbances propagate in a non-homogeneous flowing fluid. Subject to suitable restrictions, this question can be answered by invoking the language of Lorentzian differential geometry. This paper begins with a pedagogical derivation of the following result: if the fluid is barotropic and inviscid, and the flow is irrotational (though possibly time dependent), then the equation of motion for the velocity potential describing a sound wave is identical to that for a minimally coupled massless scalar field propagating in a (3 + 1)-dimensional Lorentzian geometry ψ ≡ 1 √ −g ∂ µ √ −g g µν ∂ ν ψ = 0. The acoustic metric g µν (t, x) governing the propagation of sound depends algebraically on the density, flow velocity, and local speed of sound. Even though the underlying fluid dynamics is Newtonian, non-relativistic, and takes place in flat space plus time, the fluctuations (sound waves) are governed by an effective (3 + 1)-dimensional Lorentzian spacetime geometry. This rather simple physical system exhibits a remarkable connection between classical Newtonian physics and the differential geometry of curved (3 + 1)-dimensional Lorentzian spacetimes, and is the basis underlying a deep and fruitful analogy between the black holes of Einstein gravity and supersonic fluid flows. Many results and definitions can be carried over directly from one system to another. For example, it will be shown how to define the ergosphere, trapped regions, acoustic apparent horizon, and acoustic event horizon for a supersonic fluid flow, and the close relationship between the acoustic metric for the fluid flow surrounding a point sink and the Painlevé-Gullstrand form of the Schwarzschild metric for a black hole will be exhibited. This analysis can be used either to provide a concrete non-relativistic analogy for black-hole physics, or to provide a framework for attacking acoustics problems with the full power of Lorentzian differential geometry.

Classical and Quantum …, 1999

2018

We numerically study the gravitational collapse of a massless scalar field with spherical symmetry in Einstein-aether theory, and show that apparent, spin-0, and dynamical universal horizons (dUHs) can be all formed. The spacetime and the aether field are well-behaved and regular, including regions nearby these horizons (but away from the center of spherical symmetry). The spacetime outside the apparent and spin-0 horizons settles down to a static configuration, and some of such resulting static black holes were already found numerically in the literature. On the other hand, the proper distance of the outermost dUH from the apparent (or spin-0) horizon keeps increasing on aether-orthogonal time slices. This indicates that the outermost dUH is evolving into the causal boundary, even for excitations with large speeds of propagation.

Physical Review Letters, 2013

Holography grew out of black hole thermodynamics, which relies on the causal structure and general covariance of general relativity. In Einstein-aether theory, a generally covariant theory with a dynamical timelike unit vector, every solution breaks local Lorentz invariance, thereby grossly modifying the causal structure of gravity. However, there are still absolute causal boundaries, called "universal horizons", which are not Killing horizons yet obey a first law of black hole mechanics and must have an entropy if they do not violate a generalized second law. We couple a scalar field to the timelike vector and show via the tunneling approach that the universal horizon radiates as a blackbody at a fixed temperature, even if the scalar field equations also violate local Lorentz invariance. This suggests that the class of holographic theories may be much broader than currently assumed.

2006

In our previous papers the first step was made to the construction of a global wave function on the configuration space of a self-gravitating shell. The asymptotic behaviour of analytical wave functions at the infinities was analyzed. As a result, a discrete mass spectrum of a quantum black hole and a discrete spectrum for the Hawking radiation were found. In the present paper we study a global quasiclassical solution inside and outside the horizon. The result is rather unexpected: for a quasiclassical solution with two waves of equal amplitudes under the horizon we obtain, in the outer region of the black hole, ingoing and outgoing waves with the amplitudes Zin and Zout such that Z 2 in /Z 2 out = exp{−δA/(4m 2 pl)} where A is the black hole horizon area. This result exactly coincides with the main result of the Hartle and Hawking consideration [21], from which one can derive the value of the black hole temperature and entropy.

arXiv (Cornell University), 2023

Black and white holes play remarkably contrasting roles in general relativity versus observational astrophysics. While there is observational evidence for the existence of compact objects that are "cold, dark, and heavy", which thereby are natural candidates for black holes, the theoretically viable time-reversed variants-the "white holes"-have nowhere near the same level of observational support. Herein we shall explore the theoretical possibility that the connection between black and white holes is much more intimate than commonly appreciated. We shall first construct "horizon penetrating" coordinate systems that differ from the standard curvature coordinates only in a small near-horizon region, thereby emphasizing that ultimately the distinction between black and white horizons depends only on near-horizon physics. We shall then construct an explicit model for a "black-to-white transition" where all of the nontrivial physics is confined to a compact region of spacetime-a finite-duration finite-thickness, (in principle arbitrarily small), region straddling the naïve horizon. Moreover we shall show that it is possible to arrange the "black-to-white transition" to have zero action-so that it will not be subject to destructive interference in the Feynman path integral. This then raises the very intriguing possibility that astrophysical black holes might be interpretable in terms of a quantum superposition of black and white horizons-a "gray" horizon.

Physical Review D, 2018

We numerically study the gravitational collapse of a massless scalar field with spherical symmetry in Einstein-aether theory, and show that apparent, spin-0 and dynamical universal horizons (dUHs) can be all formed. The spacetime and the aether field are well-behaved and regular, including regions nearby these horizons (but away from the center of spherical symmetry). The spacetime outside the apparent and spin-0 horizons settles down to a static configuration, and some of such resulting static black holes were already found numerically in the literature. On the other hand, the proper distance of the outermost dUH from the apparent (or spin-0) horizon keeps increasing on aether-orthogonal time slices. This indicates that the outermost dUH is evolving into the causal boundary, even for excitations with large speeds of propagation.