[Paper Review] Black Hole Formation and Growth: Simulations in General Relativity

Stuart L. Shapiro|ArXiv.org|Nov 9, 2007

Pulsars and Gravitational Waves Research40 references3 citations

TL;DR

This paper presents numerical simulations in full general relativity to study black hole formation and growth, focusing on stellar collapse, binary mergers, and supermassive black hole seed accretion. It demonstrates that relativistic MHD accretion disks enable efficient black hole growth to supermassive scales, while standard thin disks fail under high-redshift constraints, highlighting the need for advanced simulations to resolve early universe black hole formation.

ABSTRACT

Black holes are popping up all over the place: in compact binary X-ray sources and GRBs, in quasars, AGNs and the cores of all bulge galaxies, in binary black holes and binary black hole-neutron stars, and maybe even in the LHC! Black holes are strong-field objects governed by Einstein's equations of general relativity. Hence general relativistic, numerical simulations of dynamical phenomena involving black holes may help reveal ways in which black holes can form, grow and be detected in the universe. To convey the state-of-the art, we summarize several representative simulations here, including the collapse of a hypermassive neutron star to a black hole following the merger of a binary neutron star, the magnetorotational collapse of a massive star to a black hole, and the formation and growth of supermassive black hole seeds by relativistic MHD accretion in the early universe.

Motivation & Objective

• To understand the formation and growth mechanisms of black holes across cosmic time using full general relativistic simulations.
• To investigate whether early supermassive black hole seeds can grow to observed masses by z ≈ 6.43 via accretion and mergers.
• To assess the viability of different accretion models—relativistic MHD vs. standard thin disks—under cosmological constraints.
• To evaluate the role of black hole spin evolution and radiation efficiency in limiting or enabling rapid mass growth.
• To determine the implications of seed formation redshift on the feasibility of supermassive black hole formation by high redshift quasars.

Proposed method

• Utilizes the 3+1 decomposition of Einstein’s field equations with the BSSN formulation to solve the evolution of spacetime and matter fields.
• Employs numerical relativity to simulate hypermassive neutron star collapse following binary neutron star mergers.
• Models magnetorotational collapse of massive stars to black holes using relativistic hydrodynamics and magnetic fields.
• Simulates relativistic MHD accretion disks around black hole seeds to compute mass amplification over cosmic time.
• Applies Eddington-limited accretion with variable radiation efficiency εL = 1 and constant εM to compute growth factors.
• Compares growth outcomes across different initial seed masses (100–600 M☉) and redshifts (Zi ≳ 40), incorporating merger-assisted growth (×10⁴).

Experimental results

Research questions

• RQ1 Can relativistic MHD accretion disks grow black hole seeds to 10⁹ M☉ by z ≈ 6.43, the redshift of the most distant known quasar?
• RQ2 How does the growth efficiency of standard thin disks compare to relativistic MHD disks when accounting for photon recapture and spin evolution?
• RQ3 What is the minimum initial seed mass compatible with observed supermassive black hole masses at high redshift?
• RQ4 How sensitive is black hole growth to the redshift of seed formation, particularly if seeds form after Zi ≈ 40?
• RQ5 Can black hole growth via gas accretion alone explain the existence of 10⁹ M☉ black holes at z ≈ 6.43 if the seed mass is below 600 M☉?

Key findings

• Relativistic MHD accretion disks enable black hole mass amplification sufficient to grow 100–600 M☉ seeds to 10⁹ M☉ by z ≈ 6.43, satisfying observational constraints.
• Standard thin disks that account for photon recapture allow only marginal growth, while those driving maximal spin are insufficient to achieve required mass amplification.
• For seed masses below 600 M☉, gas accretion via standard thin disks is ruled out as a viable growth mechanism by z ≈ 6.43.
• A black hole driven to spin equilibrium by a turbulent MHD disk accretes with low enough efficiency to grow to supermassive size within the observed cosmic timeline.
• The required growth is feasible only if the seed forms at Zi ≳ 40; growth becomes significantly constrained only if formation occurs at Zi ≲ 20–25.
• The discovery of a quasar at z > 6.43 would challenge current models of black hole growth from Pop III star remnants, underscoring the need for refined simulations with full radiation transfer.