A new energy upper bound for AdS black holes inspired by free field theory

Cheamsawat, Krai; Gibbons, G. W.; Wiseman, Toby

doi:10.1088/1361-6382/ab56f3

Cited by 4 publications

(5 citation statements)

References 35 publications

(111 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The boundary geometries have been chosen to be maximally symmetric for simplicity. However, investigating how bulk quantities (in particular the energy [33,34]) respond to perturbations in the shape of the boundary spheres can lead to important observations, so it might be worth exploring such perturbations in our case also. In particular, a large class of less symmetric Einstein metrics on S 2 × S 3 are now known (see e.g.…”

Section: Discussionmentioning

confidence: 99%

An infinity of black holes

Ye¹,

Wang²,

Horowitz³

2022

Class. Quantum Grav.

View full text Add to dashboard Cite

In general relativity (without matter), there is typically a one parameter family of static, maximally symmetric black hole solutions labelled by their mass. We show that there are situations with many more black holes. We study asymptotically anti-de Sitter solutions in six and seven dimensions having a conformal boundary which is a product of spheres cross time. We show that the number of families of static, maximally symmetric black holes depends on the ratio, λ, of the radii of the boundary spheres. As λ approaches a critical value, λc, the number of such families becomes inﬁnite. In each family, we can take the size of the black hole to zero, obtaining an inﬁnite number of static, maximally symmetric non-black hole solutions. We discuss several applications of these results, including Hawking-Page phase transitions and the phase diagram of dual ﬁeld theories on a product of spheres, new positive energy conjectures, and more.

show abstract

Section: Discussionmentioning

confidence: 99%

An infinity of black holes

Ye¹,

Wang²,

Horowitz³

2022

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…12 An example of a spacetime with S → 0 as T → 0 is the zero temperature limit of toroidal black hole which ends on the quotient of the singular Poincare horizon in the IR [37]. For a spacetime with finite entropy as T → 0, an example is the zero temperature limit of topological black hole [38] whose bulk geometry ends on the degenerate horizon.…”

Section: Zero Temperaturementioning

confidence: 99%

A new energy bound for Einstein-Scalar theory in AlAdS$_4$ and holographic bound for deformed CFT$_3$

Cheamsawat

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In this work, we derive an upper bound on energetic quantities, namely vacuum energy and free energy, for static solutions of Einstein-Scalar theory in four dimensional asymptotically locally Anti-de Sitter(AlAdS) spacetime with a nontrivial scalar potential where the scalar field mass parameter(m 2 ) is equal to 0 or -2. This system is the holographic dual of strongly coupled conformal field theory(CFT) in three dimensions being deformed by a relevant or marginal scalar operator of conformal dimension ∆ = 1, 2, 3. The bound is derived from a purely gravitational perspective regardless of the inhomogeneity of the static conformal boundary of AlAdS and the source of the deformation. We demonstrate the bound in simple settings and check the consistency with the known previous bounds.

show abstract

“…Holographic CFT (S , g) or (R 2 , g) T = 0 ∆F q ≤ 0 [10][11][12] Holographic CFT (R 2 ,ḡ + h) T ≥ 0 ∆F q ≤ [13] Holographic CFT (R 2 , long wavelength) T ≥ 0 ∆F q ≤ 0 [13] Holographic CFT (T 2 , g) T ≥ 0 ∆E ≤ 0 [14] Unitary CFT (S 2 ,ḡ + h) or (R 2 ,ḡ + h) T = 0 ∆F q ≤ 0 [15] Free scalar or fermion (R 2 ,ḡ + h) T ≥ 0 ∆F q ≤ 0 [16] Free scalar or fermion (R 2 , long wavelength) T ≥ 0 ∆F q ≤ 0 [13] Table 1. A summary of results for the free energy F q (or just energy E in the fourth row) for various types QFTs at various temperatures.…”

Section: Introductionmentioning

confidence: 99%

Does the round sphere maximize the free energy of (2+1)-dimensional QFTs?

Fischetti

Wallis

Wiseman

2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We examine the renormalized free energy of the free Dirac fermion and the free scalar on a (2+1)-dimensional geometry ℝ × Σ, with Σ having spherical topology and prescribed area. Using heat kernel methods, we perturbatively compute this energy when Σ is a small deformation of the round sphere, finding that at any temperature the round sphere is a local maximum. At low temperature the free energy difference is due to the Casimir effect. We then numerically compute this free energy for a class of large axisymmetric deformations, providing evidence that the round sphere globally maximizes it, and we show that the free energy difference relative to the round sphere is unbounded below as the geometry on Σ becomes singular. Both our perturbative and numerical results in fact stem from the stronger finding that the difference between the heat kernels of the round sphere and a deformed sphere always appears to have definite sign. We investigate the relevance of our results to physical systems like monolayer graphene consisting of a membrane supporting relativistic QFT degrees of freedom.

show abstract

A new energy upper bound for AdS black holes inspired by free field theory

Cited by 4 publications

References 35 publications

An infinity of black holes

An infinity of black holes

A new energy bound for Einstein-Scalar theory in AlAdS$_4$ and holographic bound for deformed CFT$_3$

Does the round sphere maximize the free energy of (2+1)-dimensional QFTs?

Contact Info

Product

Resources

About