Are there hyperentropic objects?

Bekenstein, Jacob D.

doi:10.1103/physrevd.70.121502

Cited by 366 publications

(671 citation statements)

References 23 publications

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“…This result has been generalised to standard scalar-tensor theories [9] (see also earlier work by Bekenstein with the extra assumption of spherical symmetry [10,11]). …”

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Black Hole Hair in Generalized Scalar-Tensor Gravity

2014

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The most general action for a scalar field coupled to gravity that leads to second order field equations for both the metric and the scalar -Horndeski's theory -is considered, with the extra assumption that the scalar satisfies shift symmetry. We show that in such theories the scalar field is forced to have a nontrivial configuration in black hole spacetimes, unless one carefully tunes away a linear coupling with the Gauss-Bonnet invariant. Hence, black holes for generic theories in this class will have hair. This contradicts a recent no-hair theorem, which seems to have overlooked the presence of this coupling.PACS numbers: 04.70. Bw, 04.50.Kd In general relativity, black hole spacetimes are described by the Kerr metric, so long as they are stationary, asymptotically flat, and devoid of any matter in their surroundings [1]. Stationarity is a reasonable assumption for black holes that are thought to be quiescent as endpoints of gravitational collapse. Astrophysical black holes are certainly not asymptotically flat, but one can invoke separation of scales in order to argue that the cosmological background should not seriously affect local physics and hence the structure of black holes. Finally, black holes can also carry an electromagnetic charge in the presence of an electromagnetic field. It has been conjectured that they cannot carry any other charges, which are colloquially referred to as hair [2][27]. The no-hair conjecture was inspired by the uniqueness theorems for black hole solutions in general relativity [4][5][6][7].Hawking has proven that black holes cannot carry scalar charge, provided that the scalar couples to the metric minimally or as described by Brans-Dicke theory [8]. This result has been generalised to standard scalar-tensor theories [9] (see also earlier work by Bekenstein with the extra assumption of spherical symmetry [10,11]).All of these proofs actually demonstrate that the scalar has to be constant in a black hole spacetime, which is a stronger statement. Indeed, in principle, the scalar could have a nontrivial configuration without the black hole carrying an extra (independent) charge. This is sometime referred to as "hair of the second kind". The distinction is important if one is interested in the number of parameters that fully characterise the spacetime. But, a nontrivial configuration of the scalar is usually enough to imply that the black hole spacetime will not be a solution to Einstein's equations in vacuum, and hence it differs from the black holes of general relativity.The known proofs do not apply to theories with more general coupling between the metric and the scalar, or derivative self-interactions of the scalar. Hence, they do not cover the most general scalar-tensor theory that leads to second-order field equations, known as Horndeski theory [12]. Restricting attention to theories with second order field equations is justified, as higher order derivative models are generically plagued by the Ostrogradski instability [13]. Models that belong to this class have lately ...

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“…This result has been generalised to standard scalar-tensor theories [9] (see also earlier work by Bekenstein with the extra assumption of spherical symmetry [10,11]). …”

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confidence: 99%

Black Hole Hair in Generalized Scalar-Tensor Gravity

2014

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“…For the case of black holes, as already said above, Bekenstein was the first to state that the adiabatic invariants are the black hole horizon areas [9,10]. Exploiting the idea of adiabatic invariants and the statement by Bekenstein [8], Kunstatter [11] derived for the d(≥ 4)-dimensional Schwarzschild black hole an equally spaced entropy spectrum.…”

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“…However, it was proven by Bekenstein [8,9] and others [15,16] that the area spectrum of Kerr black hole is discrete and uniformly spaced. Therefore, it was concluded that the function that was used in the above-mentioned computation as real part of the asymptotic quasinormal frequencies of Kerr black hole, i.e.…”

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Area spectrum of rotating black holes via the new interpretation of quasinormal modes

Vagenas¹

2008

J. High Energy Phys.

110

114

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Motivated by the recent work on a new physical interpretation of quasinormal modes by Maggiore, we utilize this new proposal to the interesting case of Kerr black hole. In particular, by modifying Hod's idea, the resulting black hole horizon area is quantized and the resulting area quantum is in full agreement with Bekenstein's result. Furthermore, in an attempt to show that the area spectrum is equally spaced, we follow Kunstatter's method. We propose a new interpretation as a result of Maggiore's idea, for the frequency that appears in the adiabatic invariant of a black hole. The derived area spectrum is similar to that of the quantum-corrected Kerr black hole but it is not equally spaced.Since the onset of General Relativity black holes have been a matter of major concern for the scientific community. This interest is twofold. On one hand, black holes are astrophysical objects whose fingerprints will be observed on recent or future detectors for gravitational waves e.g. LIGO [1] and VIRGO [2]. On the other hand, black holes have always been a test bed for any proposed scheme for a quantum theory of gravity. It is evident that it would be of great importance for quantum gravity (and not only) if the superficially distinct (astrophysical vs theoretical) aspects could be reconciled. Hod was one of the first to make such a phenomenological work [3]. He combined the perturbations of astrophysical black holes with the principles of Quantum Mechanics and Statistical Physics in order to derive the quantum of the black hole area spectrum. Following this line of thought, Kerr black holes are the most interesting black hole solutions since from the astrophysical point of view are the most important ones while from the purely theoretical point of view are more complicated than the simple Schwarzschild black hole.The metric of a four-dimensional Kerr black hole given in Boyer-Lindquist coordinates iswhere, as always, M is the mass of the black hole, J is the angular momentum of the black hole, a is the specific angular momentum defined as J/M , Σ = r 2 + a 2 cos 2 θ, and ∆ = r 2 − 2M r + a 2 . The roots of ∆ are given bywhere r + is the radius of the event (outer) black hole horizon and r − is the radius of the inner black hole hori- * Electronic address: evagenas@academyofathens.gr zon. The Kerr black hole is rotating with angular velocity (evaluated on the event black hole horizon)Furthermore, the horizon area and the Hawking temperature of Kerr black hole (in gravitational units) are given, respectively, byandAs mentioned before, Hod managed to derive the quantum of the area spectrum using the Bohr's Correspondence principle and the complex spectrum of the quasinormal modes that correspond to the perturbation equation of Schwarzschild black hole. The resulting quantum was of the form [3]where l p is the Planck length. Hod's idea 1 rejuvenated the interest of the research community for the quantization of the black hole area spectrum and subsequently for a derivation of black hole entropy from Statistical Physics. Actua...

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“…Consequently, they argued that the BEB does not have to be postulated as a separate requirement in addition to the GSL. Responding to their arguments Bekenstein [4] has argued that it is not always obvious in a particular example how the system avoids violating the bound and analyzed in detail several of the purported counterexamples of this type and demonstrated in each case the specific mechanism enforcing the bound.…”

Section: Introduction a What Are Entropy Bounds?mentioning

confidence: 99%

Cosmological Entropy Bounds

Brustein

Lecture Notes in Physics

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I review some basic facts about entropy bounds in general and about cosmological entropy bounds. Then I review the Causal Entropy Bound, the conditions for its validity and its application to the study of cosmological singularities. This article is based on joint work with Gabriele Veneziano and subsequent related research. I. TO GABRIELEOn the occasion of your 65th birthday may you continue to find joy in science and life as you have always had, and continue to help us understand our universe with your creative passion and vast knowledge. It is a pleasure and an honor to contribute to this volume and present one of the subjects among your many interests. Thank you for explaining to me why entropy bounds are interesting and for your collaboration on this and other subjects. II. INTRODUCTION A. What are entropy bounds?The second law of thermodynamics states that the entropy of a closed system tends to grow towards its largest possible value. But what is this maximal value? Entropy bounds aim to answer this question.Bekenstein [1] has suggested that for a system of energy E whose size R is larger than its gravitational radius R > R g ≡ 2G N E, entropy is bounded by S ≤ ER/h = R g R l −2 P .Here l P is the Planck length. This is known as the Bekenstein entropy bound (BEB).Entropy bounds are closely related to black hole (BH) thermodynamics and their interplay with their "normal" environment. They are also probably associated with instabilities to forming BH's, however, this has not been proved in an explicit calculation. The original argument of Bekenstein was based on the Geroch process: a thought experiment in which a small thermodynamic system is moved from infinity into a BH. The small system is lowered slowly until it is just outside the BH horizon, and then falls in. By requiring that the generalized second law (GSL) will not be violated one gets inequality (1).A long debate about the relationship between entropy bounds and the GSL has been going on. On one side Unruh, Wald and others [2,3] have argued that the GSL holds automatically, so that entropy bounds cannot be inferred from situations where the law seems to be violated. They argue that the microphysics will eventually take care of any apparent violation. Consequently, they argued that the BEB does not have to be postulated as a separate requirement in addition to the GSL. Responding to their arguments Bekenstein 2[4] has argued that it is not always obvious in a particular example how the system avoids violating the bound and analyzed in detail several of the purported counterexamples of this type and demonstrated in each case the specific mechanism enforcing the bound.Holography [5] (see below) suggests that the maximal entropy of any system is bounded by S HOL ≤ Al −2 P , where A is the area of the space-like surface enclosing a certain region of space. For systems of limited gravity R > R g , and since A = R 2 , the BEB implies the holography bound. Physics up to scales of about 1 TeV is very well described in terms of quantum field theory,...

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Are there hyperentropic objects?

Cited by 366 publications

References 23 publications

Black Hole Hair in Generalized Scalar-Tensor Gravity

Black Hole Hair in Generalized Scalar-Tensor Gravity

Area spectrum of rotating black holes via the new interpretation of quasinormal modes

Cosmological Entropy Bounds

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