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T16-3 φ-黑洞几何形式化规范

1. 基础数学对象​

1.1 φ-Schwarzschild度量​

class PhiSchwarzschildMetric:
    def __init__(self, mass: 'PhiNumber'):
        self.M = mass  # φ-编码的黑洞质量
        self.phi = (1 + np.sqrt(5)) / 2
        self.r_h = self.M * PhiNumber(2)  # 事件视界
        
    def metric_component_tt(self, r: 'PhiNumber') -> 'PhiNumber':
        """时间-时间分量: g_tt = -(1 - 2M/r)"""
        
    def metric_component_rr(self, r: 'PhiNumber') -> 'PhiNumber':
        """径向-径向分量: g_rr = (1 - 2M/r)^{-1}"""
        
    def metric_component_angular(self, r: 'PhiNumber') -> 'PhiNumber':
        """角度分量: g_θθ = r^2, g_φφ = r^2 sin^2θ"""
        
    def is_horizon(self, r: 'PhiNumber') -> bool:
        """检查是否在事件视界上"""
        
    def recursive_depth(self, r: 'PhiNumber') -> 'PhiNumber':
        """计算递归深度"""

1.2 φ-Kerr度量​

class PhiKerrMetric:
    def __init__(self, mass: 'PhiNumber', angular_momentum: 'PhiNumber'):
        self.M = mass
        self.J = angular_momentum
        self.a = self.J / self.M  # 角动量参数
        self.phi = (1 + np.sqrt(5)) / 2
        
    def delta(self, r: 'PhiNumber') -> 'PhiNumber':
        """Δ = r^2 - 2Mr + a^2"""
        
    def sigma(self, r: 'PhiNumber', theta: float) -> 'PhiNumber':
        """Σ = r^2 + a^2 cos^2θ"""
        
    def metric_components(self, r: 'PhiNumber', theta: float) -> Dict[str, 'PhiNumber']:
        """返回所有度量分量"""
        
    def horizon_radii(self) -> Tuple['PhiNumber', 'PhiNumber']:
        """返回内外视界半径 r_±"""
        
    def ergosphere_boundary(self, theta: float) -> 'PhiNumber':
        """能层边界"""

1.3 φ-事件视界​

class PhiEventHorizon:
    def __init__(self, metric: Union['PhiSchwarzschildMetric', 'PhiKerrMetric']):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def horizon_radius(self) -> 'PhiNumber':
        """计算视界半径"""
        
    def surface_area(self) -> 'PhiNumber':
        """计算视界面积"""
        
    def surface_gravity(self) -> 'PhiNumber':
        """计算表面引力"""
        
    def verify_no_11_constraint(self) -> bool:
        """验证视界参数满足no-11约束"""

2. 几何量计算​

2.1 φ-测地线​

class PhiGeodesic:
    def __init__(self, metric: 'PhiSchwarzschildMetric'):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def christoffel_symbols(self, r: 'PhiNumber') -> Dict[Tuple[int, int, int], 'PhiNumber']:
        """计算Christoffel符号Γ^μ_ρσ"""
        
    def geodesic_equation(self, position: List['PhiNumber'], 
                         velocity: List['PhiNumber']) -> List['PhiNumber']:
        """测地线方程 d²x^μ/dτ² + Γ^μ_ρσ dx^ρ/dτ dx^σ/dτ = 0"""
        
    def conserved_quantities(self, trajectory: List[List['PhiNumber']]) -> Dict[str, 'PhiNumber']:
        """计算守恒量：能量和角动量"""

2.2 φ-曲率张量​

class PhiCurvatureTensor:
    def __init__(self, metric: 'PhiSchwarzschildMetric'):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def riemann_tensor(self, r: 'PhiNumber') -> 'PhiTensor':
        """计算Riemann曲率张量R^ρ_σμν"""
        
    def ricci_tensor(self, r: 'PhiNumber') -> 'PhiTensor':
        """计算Ricci张量R_μν"""
        
    def ricci_scalar(self, r: 'PhiNumber') -> 'PhiNumber':
        """计算Ricci标量R"""
        
    def kretschmann_scalar(self, r: 'PhiNumber') -> 'PhiNumber':
        """计算Kretschmann标量R_μνρσR^μνρσ"""

2.3 φ-黑洞熵​

class PhiBlackHoleEntropy:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.G_phi = PhiNumber(1.0)  # φ-引力常数
        
    def bekenstein_hawking_entropy(self, horizon: 'PhiEventHorizon') -> 'PhiNumber':
        """计算Bekenstein-Hawking熵 S = A/(4G)"""
        
    def verify_quantization(self, entropy: 'PhiNumber') -> bool:
        """验证熵的φ-量子化"""
        
    def entropy_bound(self, energy: 'PhiNumber', radius: 'PhiNumber') -> 'PhiNumber':
        """计算熵界 S ≤ 2πER"""

3. 黑洞过程​

3.1 φ-黑洞形成​

class PhiBlackHoleFormation:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def gravitational_collapse(self, initial_mass: 'PhiNumber', 
                              initial_radius: 'PhiNumber') -> 'PhiSchwarzschildMetric':
        """引力坍缩形成黑洞"""
        
    def critical_density(self, radius: 'PhiNumber') -> 'PhiNumber':
        """临界密度 ρ_c = 3/(8πGr²)"""
        
    def collapse_time(self, initial_conditions: Dict) -> 'PhiNumber':
        """坍缩时间尺度"""

3.2 φ-Penrose过程​

class PhiPenroseProcess:
    def __init__(self, kerr_metric: 'PhiKerrMetric'):
        self.metric = kerr_metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def ergosphere_volume(self) -> 'PhiNumber':
        """计算能层体积"""
        
    def max_energy_extraction(self) -> 'PhiNumber':
        """最大能量提取"""
        
    def particle_trajectory(self, initial_state: Dict) -> List[List['PhiNumber']]:
        """粒子在能层中的轨迹"""

3.3 φ-黑洞合并​

class PhiBlackHoleMerger:
    def __init__(self, bh1: 'PhiSchwarzschildMetric', bh2: 'PhiSchwarzschildMetric'):
        self.bh1 = bh1
        self.bh2 = bh2
        self.phi = (1 + np.sqrt(5)) / 2
        
    def final_mass(self) -> 'PhiNumber':
        """合并后的质量"""
        
    def radiated_energy(self) -> 'PhiNumber':
        """辐射的引力波能量"""
        
    def final_spin(self) -> 'PhiNumber':
        """合并后的自旋"""
        
    def verify_area_theorem(self) -> bool:
        """验证面积定理"""

4. 观测量计算​

4.1 φ-黑洞阴影​

class PhiBlackHoleShadow:
    def __init__(self, metric: Union['PhiSchwarzschildMetric', 'PhiKerrMetric']):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def shadow_radius(self, observer_distance: 'PhiNumber') -> 'PhiNumber':
        """计算黑洞阴影半径"""
        
    def photon_sphere(self) -> 'PhiNumber':
        """光子球半径"""
        
    def critical_impact_parameter(self) -> 'PhiNumber':
        """临界碰撞参数"""

4.2 φ-吸积盘​

class PhiAccretionDisk:
    def __init__(self, black_hole: 'PhiSchwarzschildMetric'):
        self.bh = black_hole
        self.phi = (1 + np.sqrt(5)) / 2
        
    def isco_radius(self) -> 'PhiNumber':
        """最内稳定圆轨道半径"""
        
    def orbital_frequency(self, r: 'PhiNumber') -> 'PhiNumber':
        """轨道频率"""
        
    def disk_temperature(self, r: 'PhiNumber', accretion_rate: 'PhiNumber') -> 'PhiNumber':
        """盘温度分布"""

4.3 φ-潮汐效应​

class PhiTidalEffects:
    def __init__(self, metric: 'PhiSchwarzschildMetric'):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def tidal_tensor(self, r: 'PhiNumber') -> 'PhiTensor':
        """潮汐张量"""
        
    def tidal_force(self, r: 'PhiNumber', separation: 'PhiNumber') -> 'PhiNumber':
        """潮汐力"""
        
    def roche_limit(self, object_density: 'PhiNumber') -> 'PhiNumber':
        """洛希极限"""

5. 拓扑结构​

5.1 φ-Penrose图​

class PhiPenroseDiagram:
    def __init__(self, metric: 'PhiSchwarzschildMetric'):
        self.metric = metric
        self.phi = (1 + np.sqrt(5)) / 2
        
    def conformal_coordinates(self, r: 'PhiNumber', t: 'PhiNumber') -> Tuple['PhiNumber', 'PhiNumber']:
        """共形坐标变换"""
        
    def causal_structure(self) -> Dict[str, List['PhiNumber']]:
        """因果结构：视界、奇点、无穷远"""
        
    def null_geodesics(self) -> List[List['PhiNumber']]:
        """类光测地线"""

5.2 φ-捕获面​

class PhiTrappedSurface:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def expansion_scalar(self, surface: 'PhiSurface', 
                        direction: str) -> 'PhiNumber':
        """展开标量θ_±"""
        
    def is_trapped(self, surface: 'PhiSurface') -> bool:
        """判断是否为捕获面"""
        
    def apparent_horizon(self, spacetime: 'PhiSpacetime') -> 'PhiSurface':
        """寻找表观视界"""

6. 验证函数​

6.1 理论一致性检查​

def verify_no_11_constraint(metric: Union['PhiSchwarzschildMetric', 'PhiKerrMetric']) -> bool:
    """验证度量所有分量满足no-11约束"""
    
def verify_einstein_equations(metric: Union['PhiSchwarzschildMetric', 'PhiKerrMetric']) -> bool:
    """验证满足φ-Einstein方程"""
    
def verify_black_hole_uniqueness(m1: 'PhiNumber', a1: 'PhiNumber', 
                                 m2: 'PhiNumber', a2: 'PhiNumber') -> bool:
    """验证黑洞唯一性定理"""

6.2 数值精度检查​

def check_horizon_location(metric: 'PhiSchwarzschildMetric', 
                          tolerance: float = 1e-10) -> bool:
    """检查视界位置的数值精度"""
    
def check_conserved_quantities(geodesic: 'PhiGeodesic', 
                              trajectory: List[List['PhiNumber']]) -> float:
    """检查守恒量的误差"""

7. 关键常数​

# 物理常数（φ-单位制）
PHI = (1 + np.sqrt(5)) / 2
G_PHI = 1.0  # φ-引力常数
C_PHI = PHI   # φ-光速

# 特征长度尺度
R_SCHWARZSCHILD_PHI = lambda M: 2 * M  # Schwarzschild半径
L_PLANCK_PHI = PhiNumber("1.616e-35")  # φ-Planck长度

# 黑洞参数范围
MIN_BLACK_HOLE_MASS = L_PLANCK_PHI  # 最小黑洞质量
MAX_SPIN_PARAMETER = PhiNumber(1.0)  # 最大自旋参数 |a/M| ≤ 1

8. 错误处理​

class PhiBlackHoleError(Exception):
    """黑洞几何计算错误基类"""
    
class HorizonNotFoundError(PhiBlackHoleError):
    """找不到事件视界"""
    
class NakedSingularityError(PhiBlackHoleError):
    """裸奇点（违反宇宙监督）"""
    
class CausalityViolationError(PhiBlackHoleError):
    """因果性违反"""