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1. Brill waves with slow fall-off towards spatial infinity

   https://doi.org/10.1088/1361-6382/add5b7  

   Bieri, Lydia; Garfinkle, David; Wheeler, James (May 2025, Classical and Quantum Gravity)

   Abstract We compute families of solutions to the Einstein vacuum equations of the type of Brill waves, but with slow fall-off towards spatial infinity. We prove existence and uniqueness of solutions for physical data and numerically construct some representative solutions. We numerically construct an explicit example with slow-off which does not exhibit antipodal symmetry at spatial infinity. 

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2. Asymptotically hyperbolic Einstein constraint equations with apparent horizon boundary and the Penrose inequality for perturbations of Schwarzschild-AdS ^*

   https://doi.org/10.1088/1361-6382/acb24b  

   Khuri, Marcus; Kopiński, Jarosław (January 2023, Classical and Quantum Gravity)

   Abstract We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an application of this result, we verify the Penrose inequality for certain perturbations of Schwarzschild Anti-de Sitter black hole initial data. 

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3. Smooth extremal horizons are the exception, not the rule

   https://doi.org/10.1007/JHEP02(2025)169  

   Horowitz, Gary T; Santos, Jorge E (February 2025, Journal of High Energy Physics)

   A<sc>bstract</sc> We show that the general charged, rotating black hole in five-dimensional Einstein-Maxwell theory has a singular extremal limit. Only the known analytic solutions with exactly zero charge or zero angular momenta have smooth extremal horizons. We also consider general black holes in five-dimensional Einstein-Maxwell-Chern-Simons theory, and show that they also have singular extremal limits except for one special value of the coefficient of the Chern-Simons term (the one fixed by supergravity). Combining this with earlier results showing that extremal black holes have singular horizons in four-dimensional general relativity with small higher derivative corrections, and in anti-de Sitter space with perturbed boundary conditions, one sees that smooth extremal horizons are indeed the exception and not the rule. 

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4. Deep Einstein@Home Search for Continuous Gravitational Waves from the Central Compact Objects in the Supernova Remnants Vela Jr. and G347.3-0.5 Using LIGO Public Data

   https://doi.org/10.3847/1538-4357/ad8b9e  

   Ming, J; Papa, M A; Eggenstein, H-B; Beheshtipour, B; Machenschalk, B; Prix, R; Allen, B; Bensch, M (December 2024, The Astrophysical Journal)

   Abstract We perform a search for continuous nearly monochromatic gravitational waves from the central compact objects associated with the supernova remnants Vela Jr. and G347.3. Over 10¹⁸different waveforms are considered, covering signal frequencies between 20 and 1300 Hz (20 and 400 Hz) for G347.3-0.5 (Vela Jr.) and a very broad range of frequency derivatives. The data set used for this first search is from the second observing run of LIGO (O2). Thousands of volunteers donating compute cycles through the computing project Einstein@Home have made this endeavor possible. Following the Einstein@Home search, we perform multistage follow-ups of over 5 million waveforms. The threshold for selecting candidates from the Einstein@Home search is such that, after the multistage follow-up, we do not expect any surviving candidate due to noise. The very last stage uses a different data set, namely, the LIGO O3 data. We find no significant signal candidate for either targets. Based on this null result, for G347.3-0.5, we set the most constraining upper limits to date on the amplitude of gravitational-wave signals, corresponding to deformations below 10⁻⁶in a large part of the search band. At the frequency of best strain sensitivity, near 161 Hz, we set 90% confidence upper limits on the gravitational-wave intrinsic amplitude of $h_0^{90\%}\approx 6.2\times {10}^{-26}$. Over most of the frequency range, our upper limits are a factor of 10 smaller than the indirect age-based upper limit. For Vela Jr., near 163 Hz, we set $h_0^{90\%}\approx 6.4\times {10}^{-26}$. Over most of the frequency range, our upper limits are a factor of 15 smaller than the indirect age-based upper limit. The Vela Jr. upper limits presented here are slightly less constraining than the most recent upper limits of R. Abbott et al., but they apply to a broader set of signals. 

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5. Twisted Self-Similarity and the Einstein Vacuum Equations

   Rothman-Slapentokh, Yakov (January 2023, Communications in mathematical physics)

   In the previous works [RSR19, SR22] we have introduced a new type of self-similarity for the Einstein vacuum equations characterized by the fact that the homothetic vector field may be spacelike on the past light cone of the singularity. In this work we give a systematic treatment of this new self-similarity. In particular, we provide geometric characterizations of spacetimes admitting the new symmetry and show the existence and uniqueness of formal expansions around the past null cone of the singularity which may be considered analogues of the well-known Fefferman–Graham expansions. In combination with results from [RSR19] our analysis will show that the twisted self-similar solutions are sufficiently general to describe all possible asymptotic behaviors for spacetimes in the small data regime which are selfsimilar and whose homothetic vector field is everywhere spacelike on an initial spacelike hypersurface. We present an application of this later fact to the understanding of the global structure of Fefferman–Graham spacetimes and the naked singularities of [RSR19, SR22]. Lastly, we observe that by an amalgamation of the techniques from [RSR18, RSR19], one may associate true solutions to the Einstein vacuum equations to each of our formal expansions in a suitable region of spacetime. 

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