Spacetime geometry in higher spin gravity

By M. Ammon, M. Gutperle, Per Kraus, Eric Perlmutter. 2011

264 citations recorded by the source corpus.

Higher spin gravity is an interesting toy model of stringy geometry. Particularly intriguing is the presence of higher spin gauge transformations that redefine notions of invariance in gravity: the existence of event horizons and singularities in the metric become gauge dependent. In previous work, solutions of spin-3 gravity in the SL(3,R) × SL(3,R) Chern-Simons formulation were found, and were proposed to play the role of black holes. However, in the gauge employed there, the spacetime metric describes a traversable wormhole connecting two asymptotic regions, rather than a black hole. In this paper, we show explicitly that under a higher spin gauge transformation these solutions can be transformed to describe black holes with manifestly smooth event horizons, thereby changing the spacetime causal structure. A related aspect is that the Chern-Simons theory admits two distinct AdS3 vacua with different asymptotic W-algebra symmetries and central charges. We show that these vacua are connected by an explicit, Lorentz symmetry-breaking RG flow, of which our solutions represent finite temperature generalizations. These features will be present in any SL(N,R) × SL(N,R) Chern-Simons theory of higher spins.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/41a01492ff240f82300d4795c5f28c4a8bed0d45

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. Eric Perlmutter
2. M. Gaberdiel
3. Rajesh Gopakumar
4. Per Kraus
5. Thomas Hartman
6. M. Gutperle
7. M. Ammon
8. J. Boer

In Nuclear and High Energy Physics

1. Eric Perlmutter
2. M. Gaberdiel
3. Rajesh Gopakumar
4. Per Kraus
5. M. Gutperle
6. Thomas Hartman
7. M. Ammon
8. J. Boer

In Statistical and Nonlinear Physics

1. Eric Perlmutter
2. M. Gaberdiel
3. Rajesh Gopakumar
4. Per Kraus
5. M. Gutperle
6. M. Ammon
7. Thomas Hartman
8. J. Boer

Citations in the corpus

• Scalar fields and three-point functions in D = 3 higher spin gravity (2011, background): “For instance, there is by now a good understanding of higher spin black holes in D=3 [27,28,23,29,30]; in particular their entropy is known to match that of the dual CFT in the high temperature limit [23].”
• Thermodynamics of higher spin black holes in 3D (2012, background): “In fact the unstable branch-II attains its maximal value of spin-3 charge at zero temperature where it has non-vanishing entropy, and precisely matches the extremal solution discussed in [41, 43].”
• Minimal model holography (2012, methodology): “4 Other choices appeared in the analysis of [7, 35, 34].”
• Higher spin gravity in 3D: Black holes, global charges and thermodynamics (2012, background): “As explained in [1, 2], this solution does not fulfill the asymptotic conditions of ref.”
• Black holes and singularity resolution in higher spin gravity (2011, background): “In [15, 16, 17] such solutions were constructed.”
• Higher spin black holes from CFT (2012, methodology): “This definition has been used to construct explicit black hole solutions carrying higher spin charge [22] (see also [23, 24, 25]).”
• Elements of Vasiliev theory (2014, background): “This field has recently received great deal of attention especially in d = 3, [64–69], and develops rapidly.”
• Towards metric-like higher spin gauge theories in three dimensions (2012, methodology): “For instance, they do not include black holes with higher spin charges, as constructed in [32, 33, 35, 36], but we checked explicitly that these also solve the metric-like equations of motion.”
• Generalized black holes in three-dimensional spacetime (2014, background): “[21, 22] is actually a special case of a W (2) 3 black hole and it is therefore endowed, in addition to the gravitational charge of spin 2, with lower spin charges 1 and 3/2 rather than with the higher spin 3 charge.”
• Conical defects in higher spin theories (2011, background): “This is analogous to the situation of black hole solutions carrying higher spin charge discussed in [28, 29], where a gauge exists in which the black hole metric becomes a smooth traversable wormhole.”
• Bounding the space of holographic CFTs with chaos (2016, background): “Note that, like a higher spin black hole [94], a higher spin shock wave is no longer purely geometric: the higher spin fields φs are sourced by W .”
• Black holes in three dimensional higher spin gravity: a review (2012, methodology): “In [70,71] it was shown that if the holonomy conditions are satisfied, there exists a higher spin gauge transformation which makes the solution manifestly a black hole, i.”
• Partition functions of higher spin black holes and their CFT duals (2011, methodology): “Here, extending previous work [17,18], we focus on the D=2+1 dimensional higher spin theory [19,20,21], and we will consider black holes that generalize the BTZ solution [22]; see [23,24,25] for other work on black holes in higher spin gravity.”
• Thermodynamics of higher spin black holes in AdS3 (2013, background): “It is worth mentioning that proper black hole solutions must satisfy additional smoothness conditions that can be phrased in terms of the holonomy of the connections around the contractible cycle in the Euclidean formulation [15, 16].”
• The action for higher spin black holes in three dimensions (2012, methodology): “(2)We have not checked that this solution is the same as the one constructed in [11].”