diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index 28144af36d6ea..2182b3647533e 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -1,6 +1,8 @@
+from __future__ import annotations
+
 from typing import (
+    Callable,
     Hashable,
-    Optional,
 )
 import warnings
 
@@ -49,11 +51,12 @@ class NumericIndex(Index):
     """
 
     _default_dtype: np.dtype
+    _dtype_validation_metadata: tuple[Callable[..., bool], str]
 
     _is_numeric_dtype = True
     _can_hold_strings = False
 
-    def __new__(cls, data=None, dtype: Optional[Dtype] = None, copy=False, name=None):
+    def __new__(cls, data=None, dtype: Dtype | None = None, copy=False, name=None):
         name = maybe_extract_name(name, data, cls)
 
         subarr = cls._ensure_array(data, dtype, copy)
@@ -97,14 +100,8 @@ def _ensure_array(cls, data, dtype, copy: bool):
     def _validate_dtype(cls, dtype: Dtype) -> None:
         if dtype is None:
             return
-        validation_metadata = {
-            "int64index": (is_signed_integer_dtype, "signed integer"),
-            "uint64index": (is_unsigned_integer_dtype, "unsigned integer"),
-            "float64index": (is_float_dtype, "float"),
-            "rangeindex": (is_signed_integer_dtype, "signed integer"),
-        }
-
-        validation_func, expected = validation_metadata[cls._typ]
+
+        validation_func, expected = cls._dtype_validation_metadata
         if not validation_func(dtype):
             raise ValueError(
                 f"Incorrect `dtype` passed: expected {expected}, received {dtype}"
@@ -264,6 +261,7 @@ class Int64Index(IntegerIndex):
     _typ = "int64index"
     _engine_type = libindex.Int64Engine
     _default_dtype = np.dtype(np.int64)
+    _dtype_validation_metadata = (is_signed_integer_dtype, "signed integer")
 
 
 _uint64_descr_args = {
@@ -280,6 +278,7 @@ class UInt64Index(IntegerIndex):
     _typ = "uint64index"
     _engine_type = libindex.UInt64Engine
     _default_dtype = np.dtype(np.uint64)
+    _dtype_validation_metadata = (is_unsigned_integer_dtype, "unsigned integer")
 
     # ----------------------------------------------------------------
     # Indexing Methods
@@ -311,6 +310,7 @@ class Float64Index(NumericIndex):
     _typ = "float64index"
     _engine_type = libindex.Float64Engine
     _default_dtype = np.dtype(np.float64)
+    _dtype_validation_metadata = (is_float_dtype, "float")
 
     @property
     def inferred_type(self) -> str:
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 1e974063bd839..0a2c0820f20a3 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -94,6 +94,7 @@ class RangeIndex(NumericIndex):
 
     _typ = "rangeindex"
     _engine_type = libindex.Int64Engine
+    _dtype_validation_metadata = (is_signed_integer_dtype, "signed integer")
     _can_hold_na = False
     _range: range