[Paper Review] Modified Kerr black holes surrounded by dark matter spike

Salvatore Capozzıello, Soroush Zare+2 more|arXiv (Cornell University)|Nov 21, 2023

Black Holes and Theoretical Physics10 citations

TL;DR

The paper models Kerr-like black holes in a dark matter spike within Bumblebee gravity with a global monopole, derives Schwarzschild-like and rotating solutions via modified TOV and Newman-Janis methods, and uses EHT observations of M87* and Sgr A* to constrain the BGGM parameter.

ABSTRACT

We study supermassive black holes (SMBH), surrounded by a dark matter (DM) spike, that can be found at the centers of Milky Way and $ ext{M87}$ galaxies and are accompanied by a specific kind of topological defect. The investigation is developed within the framework of Bumblebee Gravity with a global monopole (BGGM). The dark matter spike is described by a power-law density profile. Our main objective is to assess how the background arising from spontaneous Lorentz symmetry breaking and the presence of a global monopole influence the properties of the Kerr BH within the region affected by the spike. Using a spherically symmetric static BH with BGGM properties as the seed metric, we construct a non-rotating spacetime with a DM spike, resulting in a BGGM-motivated Schwarzschild-like BH by solving the modified Tolman-Oppenheimer-Volkoff equations (TOV). Next, we extend this approach to the case of a rotating spacetime resulting in the BGGM-motivated Kerr-like BH (BGMKLBH). This approach allows us to explore the spacetime structure, and the BGMKLBH shadows. Then, using available observational data for the DM spike density and considering the effects of BGGM on $ ext{Sgr A}^{*}$ and $ ext{M87}^{*}$ SMBHs, we analyse the shapes of their shadows and put constraints on the BGGM parameter. Thus, we infer that the BGMKLBHs could be reliable candidates for the astrophysical BHs.

Motivation & Objective

• Assess how spontaneous Lorentz symmetry breaking and a global monopole affect black hole spacetime in a dark matter spike.
• Construct Schwarzschild-like and Kerr-like BGGM black hole solutions in a DM spike using two approaches (modified TOV and modified Einstein equations).
• Extend to rotating spacetimes via the modified Newman-Janis algorithm and analyze horizons, static limit surfaces, ergoregions, and shadows.
• Determine how DM spike parameters and BGGM coupling modify shadow shapes and sizes, and compare with EHT observations to constrain BGGM.

Proposed method

• Start from a spherically symmetric BGGM seed metric and introduce a DM spike with a power-law density profile.
• Solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations to obtain BGMSLBH metrics.
• Alternatively solve the modified Einstein field equations with DM spike and BGGM energy-momentum contributions (XHGW method).
• Extend to rotating metrics using the modified Newman-Janis algorithm to obtain BGMKLBH spacetimes.
• Analyze horizons, static limit surfaces, ergoregions, and shadows in the spike region.
• Use EHT shadow observations of M87* and Sgr A* to constrain the BGGM parameter q.

Experimental results

Research questions

• RQ1 How do BGGM effects and a dark matter spike modify the horizon structure and causal regions of Schwarzschild-like black holes?
• RQ2 What is the impact of the BGGM parameter and DM spike on the shadow shape and size for rotating BGGM black holes?
• RQ3 Can EHT observations of M87* and Sgr A* constrain the BGGM parameter within the DM spike framework?
• RQ4 How do two analytical approaches (modified TOV vs XHGW) compare in predicting BGMSLBH/BGMKLBH spacetimes?
• RQ5 Do the resulting shadows remain consistent with Kerr predictions under EHT constraints?

Key findings

• The BGGM parameter and DM spike modify the horizon location and shadow properties relative to Schwarzschild/Kerr cases.
• Rotating BGMSLBH spacetimes (BGMKLBH) exhibit altered horizons, SLSs, and ergoregions due to q and ρ_sp.
• Shadow deformation and size depend on spin parameter a and BGGM parameter q.
• EHT shadow data for M87* and Sgr A* allow overlapping parameter space with BGMKLBHs, suggesting BGGM black holes can be astrophysical candidates.
• Two construction methods (TOV-based and XHGW-based) provide compatible BGMSLBH/BGMKLBH solutions within the spike region, enabling constraint analysis.