---
id: wiki-2026-0508-black-hole
title: Black Hole
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Schwarzschild, Event Horizon, Singularity]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [physics, general-relativity, computation, information-theory]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: einsteinpy, astropy
---

# Black Hole

## 매 한 줄
> **"매 spacetime 의 region where escape velocity > c"**. Schwarzschild (1916) solution → Hawking radiation (1974) → EHT M87* image (2019) + Sgr A* (2022) → 매 2026 modern view: 매 information paradox 의 holographic / ER=EPR resolution 의 frontier. 매 CS 측면에서는 매 information bound, holographic encoding, computational limit 의 reference physical system.

## 매 핵심

### 매 정의 / 종류
- **Schwarzschild** (non-rotating, no charge): r_s = 2GM/c².
- **Kerr** (rotating): 매 ergosphere + frame dragging.
- **Reissner–Nordström** (charged), **Kerr–Newman** (rotating + charged).
- 매 mass 분류: stellar (5–100 M☉), intermediate (10²–10⁵), supermassive (10⁶–10¹⁰), primordial (PBH).

### 매 entropy / information
- Bekenstein–Hawking entropy: S = k·A / (4·ℓ_P²).
- 매 information 매 area 에 비례 — 매 holographic principle 의 origin.
- Hawking T = ℏc³ / (8π·G·M·k_B) — 매 radiation 의 thermal.
- 매 information paradox: 매 unitary evolution vs thermal radiation. **2020 island formula (Penington, Almheiri 등) 의 Page curve 도출**.

### 매 CS / 정보이론 연결
1. **Holographic bound**: 매 region 의 max info ≤ A / (4·ℓ_P²) bits.
2. **Computational limit**: Lloyd 2000 — 매 ultimate laptop 의 1 kg, 1 L 매 black-hole limit at 10⁵¹ ops/s.
3. **Quantum error correction**: 매 AdS/CFT 의 bulk reconstruction 의 QEC code (Almheiri-Dong-Harlow).
4. **ER=EPR**: 매 entanglement = wormhole — 매 quantum gravity 의 unification 의 hint.

## 💻 패턴

### Schwarzschild radius
```python
G, c, MSUN = 6.67430e-11, 2.99792458e8, 1.989e30
def schwarzschild_radius_m(M_solar): return 2 * G * (M_solar * MSUN) / c**2
print(schwarzschild_radius_m(1))      # 2953 m  (Sun)
print(schwarzschild_radius_m(4.3e6))  # Sgr A*
```

### Hawking temperature & lifetime
```python
import math
hbar, kB = 1.054571817e-34, 1.380649e-23
def hawking_T(M_kg): return hbar*c**3 / (8*math.pi*G*M_kg*kB)
def evap_time_s(M_kg): return 5120 * math.pi * G**2 * M_kg**3 / (hbar * c**4)
print(hawking_T(MSUN))              # ~6e-8 K
print(evap_time_s(MSUN) / 3.15e16)  # ~2e67 yr
```

### Geodesic integration (einsteinpy)
```python
from einsteinpy.geodesic import Timelike
from einsteinpy.metric import Schwarzschild
import astropy.units as u

geo = Timelike(metric="Schwarzschild", metric_params=(0,),
               position=[40, math.pi/2, 0], momentum=[0, 0, 3.83],
               steps=5500, delta=0.5, return_cartesian=True)
```

### Bekenstein–Hawking entropy
```python
lP2 = 2.612e-70  # Planck area m^2
def BH_entropy_bits(M_kg):
    rs = 2*G*M_kg/c**2
    A = 4*math.pi*rs**2
    return A / (4*lP2) / math.log(2)
print(f"{BH_entropy_bits(MSUN):.2e} bits")  # ~1e77
```

### Holographic bound check
```python
def holographic_max_bits(area_m2): return area_m2 / (4*lP2) / math.log(2)
# 매 1 m² boundary 매 ~1e69 bits maximum.
```

### Image-plane shadow radius (EHT-style)
```python
def shadow_radius_uas(M_solar, distance_kpc):
    rs = schwarzschild_radius_m(M_solar)
    shadow_m = 3*math.sqrt(3)*rs    # photon ring diameter ≈ 5.196·r_s/2
    d_m = distance_kpc * 3.086e19
    return (shadow_m / d_m) * (180/math.pi) * 3600 * 1e6
print(shadow_radius_uas(6.5e9, 16800))  # M87* ~ 42 µas
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Newtonian regime (r ≫ r_s) | Newtonian gravity |
| Static, spherical | **Schwarzschild metric** |
| Rotating astrophysical | **Kerr metric** |
| Quantum-gravity / info | **Page curve + island formula** |
| Holographic / dual CFT | **AdS/CFT** |
| Numerical merger | **Numerical Relativity (Einstein Toolkit)** |

**기본값**: 매 astrophysics 면 **Kerr**, 매 CS / info-theoretic discussion 면 **Bekenstein–Hawking + holographic bound**.

## 🔗 Graph
- 부모: [[General-Relativity]] · [[Quantum-Field-Theory]]
- 변형: [[Schwarzschild-Metric]] · [[Kerr-Metric]] · [[Primordial-Black-Hole]]
- 응용: [[Holographic-Principle]] · [[AdS-CFT]] · [[Hawking-Radiation]] · [[Gravitational-Waves]]
- Adjacent: [[Information-Paradox]] · [[Page-Curve]] · [[ER-EPR]] · [[Computational-Limit]]

## 🤖 LLM 활용
**언제**: 매 information-theoretic 한 entropy bound, 매 holographic / quantum gravity 의 thought experiment, 매 cosmology numerical estimation.
**언제 X**: 매 sci-fi narrative 의 wormhole-as-shortcut (매 traversable wormhole 의 exotic-matter 필요 — 매 separate topic).

## ❌ 안티패턴
- **"매 black hole 의 information 의 lost"**: 매 modern view 의 unitary preserved (Page curve, island formula).
- **"매 singularity 의 physical"**: 매 GR breakdown 의 indicator — 매 quantum gravity 의 expected to resolve.
- **"매 Hawking radiation 매 carries info trivially"**: 매 detailed mechanism 의 still active research (replica wormholes 2020).
- **Mixing M_BH ↔ r_s units**: 매 SI (kg, m) vs geometrized (M = G·M_kg/c²) 매 cross-check 항상.

## 🧪 검증 / 중복
- Verified (Schwarzschild 1916; Hawking 1974; Bekenstein 1973; EHT Collaboration 2019, 2022; Penington 2020).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 placeholder |
| 2026-05-10 | Manual cleanup — physics + CS info-bound + 6 patterns |
