Abstract
The advent of gravitational waves and black hole imaging has opened a new window into probing the horizon scale of black holes. An important question is whether string theory results for black holes can predict interesting and observable features that current and future experiments can probe. In this article I review the budding and exciting research being done on understanding the possibilities of observing signals from fuzzballs, where black holes are replaced by string-theoretic horizon-scale microstructure. In order to be accessible to both string theorists and black hole phenomenologists, I give a brief overview of the relevant observational experiments as well as the fuzzball paradigm in string theory and its explicitly constructable solutions called microstate geometries.
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Notes
An alternative to \(\epsilon \) is to define a length scale \(R_a\) at which there are large modifications to the standard evolution. This is to be considered in conjunction with a second, “hardness” length scale L, which indicates the scale on which these new, modification effects vary [7,8,9]. Such “hardness” has been conjectured to be important in determining the energy that quanta must have in order to see effects from the non-trivial fuzzball structure [10].
Mergers of neutron stars also produce gravitational waves; this was first observed in 2017 [23]. I will focus here on black hole (or ECO) mergers.
I am being a bit loose with the terminology here. The actual shadow of the black hole is usually defined to be the dark circular region in the center of the image of the black hole, which is actually not much influenced by the accretion disc [29]. The outer edge of the shadow is called the photon ring; for Schwarschild, this is \(r_\mathrm{ph} =\sqrt{27} M\). The properties of this photon ring, if measured, can give very precise information on the black hole and any possible horizon-scale structure [29,30,31,32,33].
The main uncertainty in model selection is not due to the underlying spacetime, of which it is pretty clear it must be (close to) the Kerr black hole spacetime. Rather, the details of the event horizon are effectively blurred by the complex physics of the accretion disc plasma [39]. For example, the electrons can emit non-thermal radiation that is not accounted for in most simulations, leading to flares and hot spots [40,41,42,43,44]. This also makes it hard to detect or extract features of any possible horizon-scale microstructure replacing the black hole in the spacetime [45]. Note that accretion disc plasma physics effects may also blur the ability of gravitational wave observations to perform precision strong-field gravity tests [46]. (Many thanks to B. Ripperda for elaborating this issue to me.)
Not all centers are smooth in five dimensions; the charges or parameters of a center must obey certain conditions in order to avoid being singular [83].
The quantized number of D1, D5, P excitations is related to the supergravity charges as \(Q_1 = ((2\pi )^4 g_s \alpha '^3/V_4)\, N_1\), \(Q_5 = (g_s \alpha ')\, N_5\), and \(Q_P = (\alpha '^4/(V_4 R_y^2))\, N_P\), where \(g_s\) is the (ten-dimensional) string coupling, \(\alpha '=l_s^2\) is the string length squared, and \(V_4\) is the volume of the compact four-dimensional manifold (\(T^4\) or K3) that the D5-branes wrap.
Even here, the Lunin–Mathur geometries with the most typical supertube profile are of a stringy size and so fall outside of the regime where the supergravity approximation is valid. Moreover, the most typical states will be quantum superpositions of the states described by these Lunin–Mathur supertube geometries and so are not themselves described by a geometry [17, 81, 82, 134]. Additionally, the D1/D5 system does not correspond to a black hole of finite size; rather, the ensemble of D1/D5 states corresponds to a singular geometry where the would-be horizon has zero size.
Unfortunately, there is some overloading of the terms “light ring” or “photon ring” in the literature. The conventions followed by the EHT collaboration [2, 29, 34] are that the photon ring is the edge of the black hole shadow—for Schwarschild, this is \(r=\sqrt{27}M\); see also footnote 6. However, in most gravitational wave papers such as [143], the convention is that the light ring is the smallest photon orbit radius, which for Schwarzschild is \(r=3M\).
This size is measured in an appropriate tortoise coordinate (which corresponds to the travel time of a null geodesic), see section 4.1 in [143].
A more complete list of references regarding the discussions on the claims of echo observations can be found in e.g. [6], at the start of section 1.
Note that [166, 167] considers multicentered microstate geometries where the centers are not necessarily on a line and thus a more general version of the axisymmetric multipole formulae (6)–(7) must be used. Here, I will simply adjust the nomenclature of [166, 167] to the axisymmetric notation using only \(M_\ell ,S_\ell \) (instead of general \(M_{\ell m},S_{\ell m}\)) for simplicity of presentation.
The correct definition of the magnetic Love numbers was only recently clarified [172].
Various statements can be found in the literature such as “The tidal Love numbers of black holes in four dimensions vanish”; I wish to emphasize that, to the best of my knowledge, this has only been convincingly proven for static black holes in Einstein-Maxwell gravity. It has also been shown that the Love numbers vanish for axisymmetric perturbations of slowly rotating black holes [176, 177]. Recently, it has been argued that more general gravitational perturbations lead to non-zero Love numbers for Kerr [178], although [179] claims that the Kerr Love numbers do vanish when the correct boundary conditions are used. Note also that generically, black holes in alternative theories of gravity do not have vanishing Love numbers [169, 180, 181]. See also section 1 of [182] and references therein for an overview.
Certain non-supersymmetric microstate geometries, having an actual ergoregion, can be shown to be linearly unstable [197].
I wish to thank R. Walker for discussions on this point.
Thermalization in the D1/D5 system from the dual CFT point of view and in the context of fuzzballs was discussed in [204].
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Acknowledgements
I would like to thank the editors of the General Relativity and Gravitation Topical Collection on The Fuzzball Paradigm for the invitation to contribute this review. I would also like to thank I. Bena, B. Ripperda, D. Turton, B. Vercnocke, A. Virmani, R. Walker, and N. Warner for many insightful and interesting discussions, as well as suggestions and comments on this paper. I am especially grateful to B. Vercnocke for introducing me to this research avenue and for many enthousiastic discussions over the years. I am supported by ERC Advanced Grant 787320 - QBH Structure and ERC Starting Grant 679278 - Emergent-BH.
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Mayerson, D.R. Fuzzballs and observations. Gen Relativ Gravit 52, 115 (2020). https://doi.org/10.1007/s10714-020-02769-w
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DOI: https://doi.org/10.1007/s10714-020-02769-w
Keywords
- String theory
- Supergravity
- Black holes
- Fuzzballs
- Microstate geometries
- Black hole microstates
- Gravitational waves
- Gravitational wave observations
- Black hole imaging
- EHT
- LISA
- Gravitational multipoles
- Tidal Love numbers
- Echoes
- Exotic compact objects
- Multicentered geometries
- Bubbled geometries
- Superstrata
- Quasinormal modes
- Geodesics
- Tidal effects
- Black hole observations